Perturbative effective action for the photon in noncommutative QED$_{2}$ and exactness of the Schwinger mass

TL;DR

This paper proves perturbatively that the Schwinger mass in noncommutative QED2 remains exact and uncorrected by noncommutative effects at all loop orders, using the S-matrix framework and cohomology methods.

Contribution

It demonstrates the exactness of the Schwinger mass in noncommutative QED2 to all orders, extending the analysis to all translation-invariant star products via cohomology.

Findings

Schwinger mass remains uncorrected in noncommutative QED2

S-matrix approach effectively computes higher-order corrections

Generalization to all translation-invariant star products

Abstract

In this paper, we discuss the noncommutative QED$_2$ in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass $\mu^2=\frac{e^2}{\pi}$ does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action $\Gamma[A]$ (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of $\alpha^*$-cohomology, we generalize the QED$_2$ S-matrix analysis in the Moyal star product to all translation-invariant star products.